The poll also finds those surveyed are also split on whether Senate Republicans would be justified in using the filibuster or other procedural moves to prevent a vote on a nominee they oppose.
Overall, 58% say they'd like to see the President nominate someone to the Court rather than leave the seat vacant until a new president takes office next year, 41% would prefer a vacancy.
And more -- 66% -- say that whomever Obama nominates should get a hearing in the Senate. But once that happens, 48% say that if most or all Republicans in the Senate oppose Obama's nominee, they would be justified in preventing a vote to confirm him or her.
Obama has said he does plan to nominate someone for the seat, and has called on the Senate to vote on his nominee. Kentucky Sen. Mitch McConnell, the Senate Majority Leader, has said the Senate Judiciary Committee would not hold hearings on any nominee put forward by Obama, nor would the full body vote on Obama's choice.
The public's divisions by party are almost as deep as those found in Washington. While majorities of Democrats (82%) and independents (59%) want the President to nominate someone to fill the seat, just 29% of Republicans agree. And while Republicans see blocking a vote via Senate procedure as a justifiable move (77%), independents are more divided on that question (46% say it's justified), while Democrats are not on board, just 25% say it's justified.
On one matter, however, there is partisan agreement. Majorities of Republicans (67%), independents (69%) and Democrats (60%) want the GOP leadership in the Senate to hold hearings on the nominee.
Regardless of the procedural moves involved in handling the nomination, Americans are divided on how they'd prefer Scalia's replacement to impact the Court's ideological tilt.
A plurality (37%) say Obama should nominate someone who would keep the Court about as it was, while 32% would prefer a justice who tilts the balance toward the liberal side of things, 29% more conservative. A majority of Democrats prefer a more liberal Court, while most Republicans favor a more conservative one, and independents split 30% more liberal, 26% more conservative and 40% as it was.
With the battle over a Supreme Court nominee looming, the poll finds Obama has gotten a small boost in his approval rating over the last month, with 50% now saying they approve of his performance and 46% disapproving.
That's up from 47% approval in late January, and it's the first time that measure has hit 50% in CNN/ORC polling since June 2015. The 46% who disapprove mark the lowest share to say so since 2013.
Presidential approval often ebbs and flows with impressions of the economy, but the poll suggests that isn't what's boosting Obama's ratings now.
The public has a slightly worsened view of the national economy compared with December, with 46% calling it good and 53% poor. Those figures stood at 49% good to 51% poor in December. Nearly half say their personal financial situation is better than it was a year ago (45%), up from 42% saying so last April, but the share saying they're worse off has also climbed, from 34% last April to 39% now.
The CNN/ORC Poll was conducted by telephone February 24-27 among a random national sample of 1,001 adults. Results for the full sample have a margin of sampling error of plus or minus 3 percentage points.